word problem

A school administration has instituted a rule that studentsí shorts may be no shorter than 1/5 of their height. Samís shorts were only 6 inches long, and the administration said that these shorts were 3/7 of the minimum length. How tall is Sam?

Solution

A school administration has instituted a rule that studentsí shorts may be no shorter than 1/5 of their height. Samís shorts were only 6 inches long, and the administration said that these shorts were 3/7 of the minimum length. How tall is Sam?

Start by modeling the question.
Say the student's height is equal to x.
Then the shorts may be no shorter than (1/5)*x

Now, Sam's shorts are (3/7) the length of the minimum requirement.
So, Sam's shorts are (3/7)*(1/5)*x in length
which is: (3/35)*x

Now we can set the whole thing equal to 6 since it is the fraction of the height multiplied by the height.

Set up equation:
(3/35)*x = 6

Multiply both sides by 35/3 and you get x=70 inches.
This is Sam's height, 5 feet 10 inches.